Inferring rotations using a bosonic Josephson junction

TL;DR

This work investigates how rotation modifies tunneling in a two-dimensional bosonic Josephson junction and demonstrates that tunneling observables can be used to infer rotation frequency $\Omega$, displacement $S$ from the rotation axis, and the orientation $\theta$ of an off-centered double well. Employing mean-field and many-body analyses with the MCTDHB method, the authors analyze centered, displaced, and orientation-dependent configurations, revealing that the tunneling period, transverse momentum, and angular momentum encode rotational information, while depletion/fragmentation provides an additional slow-rotation diagnostic. An analytical mapping shows that off-centered wells behave like tilted centered wells with a tilt scaling as $m\Omega^2S$, linking rotation to effective bias between wells. They further examine time-dependent rotation in the lab frame, showing switching-time dependent signatures that allow extraction of the final rotation frequency from the resulting dynamics. Overall, the paper establishes a comprehensive framework for inferring rotation frequency, radial displacement, and orientation directly from noninertial tunneling dynamics in ultracold bosonic systems.

Abstract

Rotation and quantum tunneling are fundamental concepts in physics, and their interplay in the ultracold atomic systems is of particular interest. In this theoretical work, we explore how tunneling dynamics in a bosonic Josephson junction are modified when the system is placed in a rotating, non-inertial frame. We show that the tunneling dynamics of ultracold bosons in a two-dimensional double-well potential offer an alternative pathway for inferring the rotation frequency. Using the mean-field and many-body analyses, we demonstrate that rotation strongly modifies the tunneling time period as well as the momentum and angular momentum dynamics. When the rotation axis passes through the center of the double well, the observables show distinct dynamical responses with increasing rotation frequency, enabling the rotation frequency to be assessed from changes in the tunneling dynamics. When the potential is displaced from the rotation axis, the rotation induces asymmetric tunneling and partial self-trapping, allowing both the rotation frequency and the displacement to be inferred. We further show that for an off-centered double well, the tunneling dynamics exhibit a pronounced orientation dependence, enabling the orientation of the double well to be inferred from the observed dynamics. The many-body analysis further shows that the depletion dynamics are strongly influenced by rotation, providing an additional tool for assessing the rotation frequency. Finally, we study the effect of time-dependent rotation in which the double well is gradually set into motion in the laboratory frame and identify distinct dynamical signatures that depend sensitively on the switching time. Together, these results establish a comprehensive framework for inferring the rotation frequency, radial displacement, and orientation directly from the tunneling dynamics.

Figures (8)

• Figure 1: Trap centered at the rotation axis: (a) Schematic diagram of the double-well potential centered at the rotation axis, (b) Survival probability in the left well as a function of time, (c) Expectation value of the transverse momentum per particle $\langle P_y \rangle$, and (d) Expectation value of the angular momentum per particle $\langle L_z \rangle$, shown for different rotation frequencies $\Omega$. The tunneling time period increases with $\Omega$ and eventually enters the self-trapping regime for large $\Omega$. In the full-tunneling regime, $\langle P_y \rangle$ exhibits oscillations whose period and amplitude increase with $\Omega$. $\langle L_z \rangle$ oscillates around a constant non-zero value, which also increases with $\Omega$. All results are obtained using the mean-field method, and the quantities shown are dimensionless.
• Figure 2: Assessing rotation from observables (double well at the origin): (a) The tunneling period as a function of rotation frequency $\Omega$, showing an exponential increase. (b) The oscillation amplitude of the expectation value of the transverse momentum $\langle P_y \rangle$ as a function of $\Omega$, showing a linear dependence. (c) The time-averaged expectation value of the angular momentum follows an exponential dependence on $\Omega$, which is also well approximated by a linear behavior in the low-$\Omega$ regime (black dotted curve). See the main text for further details. All quantities are dimensionless.
• Figure 3: Trap displaced from the rotation axis: (a) Schematic diagram of the double-well potential displaced by a distance $S$ from the rotation axis. (b, c) Time evolution of the survival probability in the left well for different rotation frequencies $\Omega$, shown for (b) $S=2$ and (c) $S=6$. All quantities are dimensionless.
• Figure 4: Inferring slower rotation and trap displacement: (a) Self-trapped fraction in the left well as a function of $\Omega$, extracted from the survival probability (Fig. \ref{['fig3']}). The exponential fit captures the behavior well up to $\sim 40\%$ self-trapped region, beyond which the data begin to deviate from the exponential trend. Inset: Self-trapped fraction as a function of the displacement $S$, exhibiting an exponential dependence. (b) The time-averaged expectation value of the angular momentum per particle as a function of $\Omega$, showing a linear increase in the regime where self-trapping is not prominent. Inset: Dependence of the time-averaged angular momentum $\overline{\langle L_z \rangle}$ on $S$, showing a quadratic behavior. All quantities are dimensionless.
• Figure 5: Effect of displacement and orientation relative to the rotation axis: (a) Schematic diagram of the off-center double-well potential displaced by $S$ from the rotation axis and rotated by an angle $\theta$ in the x-y plane. (b) Survival probability as a function of time for different orientations $\theta$, shown for fixed displacement $S=4$ and rotation frequency $\Omega = 0.06$. For comparison, the survival probability of the centered double well ($S=0$) is shown as a red dotted line. It coincides with the case where the double well is oriented perpendicular to the $x$-axis ($\theta = 90^\circ$). All quantities are dimensionless.